A Branch-and-Cut Procedure for the Vehicle Routing Problem with Time Windows

This paper addresses the problem of finding the minimum number of vehicles required to visit a set of nodes subject to time window and capacity constraints. The fleet is homogeneous and is located at a common depot. Each node requires the same type of service. An exact method is introduced based on...

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Bibliographic Details
Published inTransportation science Vol. 36; no. 2; pp. 250 - 269
Main Authors Bard, Jonathan F, Kontoravdis, George, Yu, Gang
Format Journal Article
LanguageEnglish
Published Linthicum, MD INFORMS 01.05.2002
Transportation Science Section of the Operations Research Society of America
Institute for Operations Research and the Management Sciences
Subjects
Algorithms
Applied sciences
Customer services
Distribution economics
Exact sciences and technology
Ground, air and sea transportation, marine construction
Heuristic
Heuristics
Income inequality
Integer programming
Integers
Linear programming
Optimal solutions
Resource allocation
Road transport
Road transportation and traffic
Time
Time windows
Transport economics
Transportation
Transportation planning, management and economics
Travel time
Traveling salesman problem
Vehicle capacity
Vehicles
Integer programming
Branch and bound method
Heuristic method
Linear programming
Routing
Numerical simulation
Road traffic
Algorithm
Route
Inequality
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Summary:This paper addresses the problem of finding the minimum number of vehicles required to visit a set of nodes subject to time window and capacity constraints. The fleet is homogeneous and is located at a common depot. Each node requires the same type of service. An exact method is introduced based on branch and cut. In the computations, ever increasing lower bounds on the optimal solution are obtained by solving a series of relaxed problems that incorporate newly found valid inequalities. Feasible solutions or upper bounds are obtained with the help of greedy randomized adaptive search procedure (GRASP). A wide variety of cuts is introduced to tighten the linear programming (LP) relaxation of the original mixed-integer program. To find violated cuts, it is necessary to solve a separation problem. A substantial portion of the paper is aimed at describing the heuristics developed for this purpose. A new approach for obtaining feasible solutions from the LP relaxation is also discussed. Numerical results for standard 50- and 100-node benchmark problems are reported.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0041-1655
1526-5447
DOI:10.1287/trsc.36.2.250.565